Logics of preference when there is no best

Well-behaved preferences (e.g., total pre-orders) are a cornerstone of several areas in artificial intelligence, from knowledge representation, where preferences typically encode likelihood comparisons, to both game and decision theories, where preferences typically encode utility comparisons. Yet weaker (e.g., cyclical) structures of comparison have proven important in a number of areas, from argumentation theory to tournaments and social choice theory. In this paper we provide logical foundations for reasoning about this type of preference structures where no obvious best elements may exist. Concretely, we compare and axiomatize a number of ways in which the concepts of maximality and optimality can be lifted to this general class of preferences. In doing so we expand the scope of the long-standing tradition of the logical analysis of preference

Social choice of convex risk measures through Arrovian aggregation of variational preferences

It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator.variational preference representation, convex risk measure, multiple priors preferences, Arrow-type preference aggregation, judgment aggregation, abstract aggregation theory, model theory, first-order predicate logic, ultrafilter, ultraproduct

DrAGON: A Framework for Computing Preferred Defense Policies from Logical Attack Graphs

Attack graphs provide formalism for modelling the vulnerabilities using a compact representation scheme. Two of the most popular attack graph representations are scenario attack graphs, and logical attack graphs. In logical attack graphs, the host machines present in the network are represented as exploit nodes, while the configurations (IDS rules, firewall policies etc.) running on them are represented as fact nodes. The actual user privileges that are possible on each of these hosts are represented as privilege nodes. Existing work provides methods to analyze logical attack graphs and compute attack paths of varying costs. In this thesis we develop a framework for analyzing the attack graph from a defender perspective. Given an acyclic logical dependency attack graph we compute defense policies that cover all known exploits that can be used by the attacker and also are preferred with respect to minimizing the impacts. In contrast to previous work on analysis of logical attack graphs where quantitative costs are assigned to the vulnerabilities (exploits), our framework allows attack graph analysis using descriptions of vulnerabilities on a qualitative scale. We develop two algorithms for computing preferred defense policies that are optimal with respect to defender preferences. Our research to the best of our knowledge is the first fully qualitative approach to analyzing these logical attack graphs and formulating defense policies based on the preferences and priorities of the defender. We provide a prototype implementation of our framework that allows logical attack graphs to be input using a simple text file (custom language), or using a GUI tool in graphical markup language (GML) format. Our implementation uses the NVD (National Vulnerability Database) as the source of CVSS impact metrics for vulnerabilities in the attack graph. Our framework generates a preferred order of defense policies using an existing preference reasoner. Preliminary experiments on various attack graphs show the correctness and efficiency of our approach

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen, Norway, July 27-30, 201